On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes

We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n + 2)-dimensional static and spherically symmetric spacetimes. They are related to the properties of the underlying spatial part of the wave operator, one of which...

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Detalles Bibliográficos
Autores principales: Gamboa Saraví, Ricardo Enrique, Sanmartino, Marcela, Tchamitchian, Philippe
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2013
Materias:
Física
Cauchy problem
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/98574
https://ri.conicet.gov.ar/11336/23632
http://iopscience.iop.org/article/10.1088/0264-9381/30/23/235014
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-98574
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Cauchy problem
spellingShingle Física
Cauchy problem
Gamboa Saraví, Ricardo Enrique
Sanmartino, Marcela
Tchamitchian, Philippe
On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
topic_facet Física
Cauchy problem
description We give simple conditions implying the well-posedness of the Cauchy problem for the propagation of classical scalar fields in general (n + 2)-dimensional static and spherically symmetric spacetimes. They are related to the properties of the underlying spatial part of the wave operator, one of which being the standard essentially self-adjointness. However, in many examples the spatial part of the wave operator turns out to be not essentially self-adjoint, but it does satisfy a weaker property that we call here quasi-essentially self-adjointness, which is enough to ensure the desired well-posedness. This is why we also characterize this second property. We state abstract results, then general results for a class of operators encompassing many examples in the literature, and we finish with the explicit analysis of some of them.
format Articulo
Preprint
author Gamboa Saraví, Ricardo Enrique
Sanmartino, Marcela
Tchamitchian, Philippe
author_facet Gamboa Saraví, Ricardo Enrique
Sanmartino, Marcela
Tchamitchian, Philippe
author_sort Gamboa Saraví, Ricardo Enrique
title On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
title_short On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
title_full On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
title_fullStr On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
title_full_unstemmed On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
title_sort on well-posedness of the cauchy problem for the wave equation in static spherically symmetric spacetimes
publishDate 2013
url http://sedici.unlp.edu.ar/handle/10915/98574
https://ri.conicet.gov.ar/11336/23632
http://iopscience.iop.org/article/10.1088/0264-9381/30/23/235014
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AT tchamitchianphilippe onwellposednessofthecauchyproblemforthewaveequationinstaticsphericallysymmetricspacetimes
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